#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2020/6/13 11:08
# @USER    : Shengji He
# @File    : ClimbingStairs.py
# @Software: PyCharm
# @Version  : Python-
# @TASK:
from math import sqrt


class Solution:
    def climbStairs(self, n: int) -> int:
        """
        You are climbing a stair case. It takes n steps to reach to the top.

        Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

        Note: Given n will be a positive integer.

        Example 1:
            Input: 2

            Output: 2

            Explanation: There are two ways to climb to the top.
                1. 1 step + 1 step

                2. 2 steps
        Example 2:
            Input: 3

            Output: 3

            Explanation: There are three ways to climb to the top.
                1. 1 step + 1 step + 1 step

                2. 1 step + 2 steps

                3. 2 steps + 1 step

        :param n: int
        :return: int
        """
        # p, q, ans = 0, 0, 1
        # for i in range(1, n + 1):
        #     p, q = q, ans
        #     ans = p + q
        # return ans
        return int((((1 + sqrt(5)) / 2) ** (n + 1) - ((1 - sqrt(5)) / 2) ** (n + 1)) / sqrt(5))


if __name__ == '__main__':
    S = Solution()
    n = 7
    print(S.climbStairs(n))
    print('done')
